A criticism of scientific knowledge is necessary when we see it being peddled as an absolutist source of knowledge. It's amusing that the same folks who worship at the altar of reason, rationale and logic, abandon it when it comes to 'belief' in science, or its currently popular avatar, scientism.
This is more common than is understood, and while not a critique of the scientific method itself, is an attempt to understand why we believe what we believe. Using metaphysics to critique physics is as old as ancient philosophy, but there are merits to recognising the limits of this particular methodology.
Let's take materialism, the theory in vogue about reality, or the belief that the gamut of knowable phenomena is exhausted by matter and energy, and that scientific knowledge occupies the pivotal position epistemologically. That only matter, energy, and matter-energy relations exist. Even if it seems futile to point out the obvious error in pre-supposing and mentioning 'relations' in a framework that fundamentally tries to do away with it, there are other salient features of this creed that raises philosophical brows.
At the outset, materialism crumbles by the might of its own supposition: that scientific knowledge is the only true knowledge. Because it is a metaphysical statement that cannot be verified by performing any scientific experiment.
Having reached this dead-end, the materialist might jump to provide real-life examples of why his theory is valid. So let's apply it to examine the most commonly accessible phenomenon known to man: consciousness. Here too, we will find that a materialist would be in deep waters. A materialist would tend to agree that the mind and body are one and the same thing. So far so good. The split between the mind and body was a false dichotomy that persisted for centuries since Descartes' intuitive concept of Cartesian dualism in the 17th century. The idea that the mental and the physical occupy different ontological planes is a deeply held belief for many even today, especially the religious nuts.
The problem really starts when the materialist tries to account for consciousness by looking for it in the brain. Till date, there has been no coherent principle or theory in neuroscience that shows how consciousness resides within the brain. Here, a materialist's best defence really is: "we don't know where consciousness comes from but we know for sure that without a physical brain, there wouldn't be any consciousness." There is no arguing with that either. The sensible rebuttal to that is: while a brain is necessary for consciousness, it is not sufficient.
For empirical evidence a materialist will point to brain scans that purport to show that anything we call consciousness is just certain "activity" or neuronal firing in select areas of the brain. In other words, the thought/emotion/intention/belief we experience is simply neuronal firing (unless they're an eliminative materialist, in which case they'd say thoughts/emotions/intentions don't exist).
The problem with this concept becomes clear with an analogy: imagine seeing footprints left behind by a walker on the beach. The act of walking precedes the footprint appearing on the sand, logically and temporally. Just like claiming that the footprint caused the walking would be preposterous, so it is with claims that identify neuronal activity with consciousness. The evidence of a tsunami — debris, floods, destruction — is not the tsunami itself. Here, the materialist commits the fundamental yet cardinal fallacy of mistaking the effect for the cause.
There are other issues too. What do we make of mathematics in the light of all this? Our materialist has two options. Either mathematics is a feature of the world, or it is a feature of the mind. We can't really say it's a property of the universe because, it would seem this 'property' has been ascribed to it. And secondly, many, many fields of mathematics describe things that don't represent anything even remotely familiar in the known world. Complexity theory, the Mandelbrot set, value of Pi. A perfect circle with the ratio of circumference does not exist in the real world. There are more irrational numbers than rational ones. Scientists deal with
imaginary numbers all the time. So where does mathematics come from? From Plato to Penrose, there are many who do not rule out a Platonic realm from where we access these truths.
The second option then, is, that mathematics is all in the mind.
Why neuroscientists of the materialist stripe swallow this is obvious. For anyone who believes that matter and energy are all that's there, this is a textbook case of applying the Occam's razor. If mathematics depends on the mind, and if you put them in the same ontological category, it would seem that mathematics would not exist outside of the mind. But we know, and it is indeed possible to deduce, that mathematical truths exist independent of the mind. The matter-hatters commit a mindless blunder when they reduce mind to matter.
Moreover, explaining our thoughts, intentionality, meaning, and qualia — the qualitative experience of sensoria— as a purely physical property will lead to circular reasoning. Applying reductio ad absurdum, let's say all our thoughts, desires, intentions, beliefs and feelings are a result of complex neuronal firings and hormonal sloshings. If this be the case, why would you trust it, since belief JUST IS another firing of the neurons and how on earth is it supposed to mean anything? For if our beliefs are just brain-states or an electro-chemical property of the brain, then even the 'belief' that beliefs are brain-states is another brain-state. One would be hard pressed to infer a truth value from a brain-state. Do the ripples in the lake have truth value? Then how do ripples in a mass of wrinkled tissue manage to do? That's what this quest is all about actually.
If brain-states have any truth value, it would seem that truths originate in the brain, corresponding to a particular state. In that case, mathematical truths would have no independent existence without the brain. If the naturalist, or materialist, holds that mathematical truths are independent of the brain, is there a mathematical realm where they exist, beyond the physical world? If so, why shouldn't there be necessary truths that transcend the physical world? If these truths can be accessed by the mind, there exist in the mind certain truths that have a non-physical origin.
The materialist is then forced to concede that meanings and beliefs are an illusion. And if one wants to take the easy way out, it is better to leave it at this. It's all an illusion. The emergent self with its attendant universe of thoughts, feelings, intentions, and QUALITATIVE EXPERIENCE, is all one big deception.
I could go on to the next wench in the materialist conception of consciousness by invoking the problem of intentionality, or the idea that the mind is able to direct itself to something that is outside of itself. Like any thought that is not self-referential — that cup of chai, your pet dog, girlfriend, the weather, book, anything really. But it is completely unnecessary at this point. When we cannot physically account for consciousness emerging from the brain, what is the point of splitting hairs about one particular property of consciousness among the millions.
Lastly, the materialist mind cannot account for QUALIA, the REDNESS of the colour red, and the FEELING of pain. Forget consciousness, we don't even know why we experience pain. Or rather, we have been unable to find a physical basis for pain. Don't get me wrong, there is a physicality to pain of course. The firing of the C-fibres in the nervous system shows up in scans when we experience pain, but that is only the footprint left behind and not the thing in itself. What is the colour of red? Is it just the 'qualitative sensoria' we experience when subjected to electromagnetic radiation of a certain wavelength (700 nm)? It is true that colour as such does not exist outside of the brain.
If you really think about it, asking if the universe follows a universal colour palette that is the same for everyone is simply a variation of that trick question about trees falling in the forest.